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lfunc_lfunctions • Show schema
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{'Lhash': '1829691916263589588227812042745', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.9238795325112867, 0.3826834323650898], 'a4': [0.0, 0.0], 'a5': [0.18406231131210887, 0.444365728291432], 'a6': [0.0, 0.0], 'a7': [0.13453123466199407, -0.13453123466199407], 'a8': [0.0, 0.0], 'a9': [0.7071067811865476, 0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.9238795325112867, -0.3826834323650898]]]], 'bad_primes': [2, 3], 'central_character': '384.337', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '2117172712894671825703057474397', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [-0.18406231131210887, -0.444365728291432], [-3.5355339059327378, 3.5355339059327378]], [[1.0, 0], 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[-77.07463914933368, -77.07463914933368]], [[1.0, 0], [0, 4.4834922210138535], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-384-32.29-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/384/2/n/a/337/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7356460480112659, 1.703155630544294, 1.6687411994593007, 1.6267215699020372, 1.5693619589086967, 1.4880774513205415, 1.3746318405721734, 1.2222197050734591, 1.026403726688859, 0.7859067949190485, 0.5032444707581902, 0.18515570242559815, -0.15723235601103605, -0.5085772306383253, -0.8498944504962046, -1.1595688213869, -1.414801888751025, -1.5934438235419324, -1.6761019375482231, -1.6483621065573582, -1.5029108566217373, -1.2413126719621772, -0.8751868789043095, 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'7.34106396002709057588087797114226', '8.849839145135126936273427361307393', '9.158096641517046465056392073529816', '10.25150357411831316131676486624325', '11.44933237081876988271358002997637'], 'prelabel': '2-384-32.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.11433154146425996, 'root_number': '0.9361842733885468 - 0.3515096104802238*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0571657707321', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44337242133926301487863037248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98217856182731216419603402603', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24387137602891532316532333764', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'bad_primes': [2, 3], 'central_character': '32.29', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/2/n/a/337/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-384-32.29-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-384-32.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.05716577073212998, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44337242133926301487863037248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1829691916263589588227812042745', 'Lhash_array': ['1829691916263589588227812042745'], 'label': '2-384-32.29-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/n/a/337/6'}